Schur sigma-groups with abelian quotient invariants (9,3)
Group Theory
2020-06-17 v1 Number Theory
Abstract
By the construction of suitable non-metabelian Schur sigma-groups S of type (9,3) with log order lo(S) = 21 and nilpotency class cl(S) = 9, evidence is provided of a new class of imaginary quadratic fields K with 3-class group Cl(3,K) ~ C(9) * C(3) and punctured principalization type kappa ~ (1,4,4;4) whose 3-class field tower consists of precisely three stages. In contrast, previous examples of three-stage towers were associated with kappa in { (1,1,2;2), (1,1,2;3), (1,1,4;2), (1,2,3;1) }, lo(S) = 9 and cl(S) = 5.
Keywords
Cite
@article{arxiv.2006.09177,
title = {Schur sigma-groups with abelian quotient invariants (9,3)},
author = {Daniel C. Mayer},
journal= {arXiv preprint arXiv:2006.09177},
year = {2020}
}
Comments
9 pages, 2 tables